Interactive examples
I display here only a few examples from large collection of Hirotaka Ebisui problems. All of them are shown in a dynamic environment. Therefore, we can experiment with these examples. However, each of them is a true theorem only in a specific context. Therefore, after moving points, or lines, outside the context limits we can find that the theorem no longer is true, and sometimes we get a new theorem.  

large product photo

Convention

  1. Green, medium lines are the starting point
  2. Thin lines, green or blue are the construction seconary lines
  3. Small points are the construction points
  4. Large yallow points are the interactivity points, move them to see what is happening with the model
  5. Red lines are the final lines with a property to prove

Example: the picture above shows construction where we start with a circle and 5 points (large yellow points), we draw 5 circles internally tangent to the large circle. The red lines are obtained last. We have to prove that they intersect in the point A.

 

Special problems